knjiga solarna energija dobra

PV GENERATOR BEHAVIOUR UNDER REAL OPERATION CONDITIONS 951
• The short-circuit current of a solar cell depends exclusively and linearly on the irradiance.
That is,
I SC (G) = I SC
∗
G G ∗ eff (20.68)
where G eff is the “effective” irradiance. This concept must take into consideration the
optical effects related to solar angle of incidence, as described in Section 20.7. Effects,
as described by equations (20.46–20.59), are as follows:
• The open-circuit voltage of a module depends exclusively on the temperature of the
solar cells T c . The voltage decreases linearly with increasing temperature. Hence,
V OC (T c ) = V ∗ OC + (T c − T ∗
c )dV OC
dT c
(20.69)
where the voltage temperature coefficient, dV OC /dT c is negative. The measurement of
this parameter used to be included in PV modules characterisation standards [51, 56] and
the corresponding value must, in principle, be also included on the manufacturer’s data
sheets. For crystalline silicon cells, dV OC /dT c is typically −2.3 mV per ◦ C and per cell.
• The series resistance is a property of the solar cells, unaffected by the
operating conditions.
• The operating temperature of the solar cell above ambient is roughly proportional to
the incident irradiance. That is,
T c = T a + C t G eff (20.70)
where the constant C t has the value:
C t = NOCT (◦ C) − 20
800 W/m 2 (20.71)
The values of NOCT for modules currently on the market varies from about 42 to 46 ◦ C,
implying a value of C t between 0.027 and 0.032 ◦ C/(W/m 2 ). When NOCT is unknown,
it is reasonable to approximate C t = 0.030 ◦ C/(W/m 2 ). This NOCT value corresponds to
mounting schemes allowing the free air convection in both sides of the PV modules,
which cannot be the case on roof-mounting arrays, that restrict some of the airflow. Then,
it has been shown [57] that the NOCT increases by about 17 ◦ Cifsomekindofback
ventilation is still allowed and up to 35 ◦ C if the modules are mounted directly on a
highly insulated roof.
Example: To illustrate the use and the usefulness of the equations of the above
sections, we shall analyse the electrical behaviour of a PV generator rated at 1780 W
(STC), made up of 40 modules, arranged 10 in series × 4 in parallel. The conditions
of operation are G eff = 700 Wm −2 and T a = 34 ◦ C. It is known that the modules have
the following characteristics under STC: ISC ∗ = 3A,V OC ∗ = 19.8 VandP M ∗ = 44.5 W.
Further, it is known that each module consists of 33 cells connected in series and that
NOCT = 43 ◦ C.
The calculations consist of the following steps:
1. Determination of the characteristic parameters of the cells that make up the
generator under STC (equations 20.63–20.67):